Digital Communication: Solutions Manual by Edward A. Lee, David G. Messerschmitt

By Edward A. Lee, David G. Messerschmitt

This complement comprises labored out recommendations to the bankruptcy finish challenge units present in Digital verbal exchange, moment Edition, ISBN 0-7923-9391-0.

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89) and substituting for Y. this becomes Multiplying out the left side. 90) and dividing by d i J. S· -So Re{

6·30. (a) This is just a matter of multiplying it out (b) Let 8(00) ="'tD(oo). 199), we get the pulses with Fourier transforms shown in figure 6-61. From this, we see that each pulse consists of three parts. Each part is a sine pulse modulated by e- j2Jrlrttrr for m = 0, I, and 2, and scaled by a complex value that depends on n. For n =0, I, and 2, we can write . h (I) = sinc (1U ([') ~ ( 1+e -j23t{.!.. +~) T 3 +e -j4Jl(.!.. 375) where sine (x) = sin(x )/x. (d) The time domain pulses are not real.

The middle of which is zero. The othec two can be found by finding the observation at which the receiver is indifferent between a decision +3 and a decision +1. 1) = Iy _11 2 _ 2021n(0A). 179) Solving this yields y =2 + ~a2In(4). 180) The thresholds are therefore at ± (2 + 'ha2In(4». 1 yields a decision £ = 1. 9-4. ;. 181) 9-S. (a) 51 =[1,O,OJ, 52 =[0,1 ,OJ, 53 =[0,0,1] . 184) transmitted] S 3Q (2,p) . 185) Pr[ error 15i Note that in both cases Pr[ error 15i transmitted] is independent of i , so 9-6.

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